Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
298 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×M16 | C2 | semidirect |
| 3. C2×#208 | C2 | semidirect |
| 4. D3×M16 | C2 | direct (N × H) |
| 5. C2×ΓL(1,𝔽25) | C2 | semidirect |
| 6. C2×D3×C8 | C2 | semidirect |
| 17. C3×M16 | C22 | semidirect |
| 18. C2×C3×C8 | C22 | semidirect |
| 19. #208 | C22 | semidirect |
| 20. C2×C3⋊C8 | C22 | semidirect |
| 21. ΓL(1,𝔽25) | C22 | semidirect |
| 22. D3×C8 | C22 | semidirect |
| 27. C2×M16 | D3 | direct (N × H) |
| 47. C3×C8 | C23 | semidirect |
| 48. C3⋊C8 | C23 | semidirect |
| 60. M16 | C2×D3 | direct (N × H) |
| 63. C2×C8 | C2×D3 | semidirect |
| 69. C2×D3 | M16 | direct (N × H) |
| 96. C8 | C22×D3 | semidirect |
| 98. C2×C3 | C2×M16 | semidirect |
| 101. D3 | C2×M16 | direct (N × H) |
| 115. C3 | C22×M16 | semidirect |
| 119. C2 | D3×M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D3 | 2 |
| C2×C3×M16 | 2 |
| C2×#208 | 2 |
| D3×M16 | 2 |
| C2×ΓL(1,𝔽25) | 2 |
| C2×D3×C8 | 2 |
| C22×M16 | 3 |